how many intergers between 299 and 501 are divisible by both 2 and 5

Question

1.) 12

2.) 20

3.) 21

4.) 100

Answer 1

The are 21 integers divisible by both 2 and 5.

They are 300, 310, 320, . . . . . , 480, 490, 500.

These are the integers which are divisible by 10 -- which is divisible by 2 and by 5.

Answer 2

about 200 integers in that range

to be divisible by 2 and 5 means be divisible by 10 (2x5)

200/10 = 20

answer has to be either 20 or 21

turns out it's 21

because we are sort of getting the end points, 300 and 500, so add 1 to 20 = 21

Answer 3

integers divisible by 5 end in 0 or 5

integers divisible by 2 must be even

So, 300, 310, 320, 330, ..., 500